III A Sports club offers two types of membership. Offer A A membership fee of 10,000,000 L.L for the first year only , after which a yearly amount of 500,000 L.L is to be paid after the first year. Denote by S, the amount paid during n years Offer B An annual membership fee of 1,000,000 L L for the first year which increases each year by 10% after the first year Also with this offer and starting the second year , a reduction of 50,000 LL is made to the amount paid to the club Denote by Un the amount, expressed in L.L paid by a member to the club , with offer B the n year Soul = 1,000,000 1 Determine the total sum Sn paid by a member who chose type A for the first n years 2 Let(,) be the sequence defined as Vn-Un-500,000 where n is a natural number greater or equal 1 a) Express Un+1 in terms of Un . b) Show that (V) is a geometric sequence whose common ratio and first term to be determined 3 Express Vn then Un in terms of n 4 Denote by S, the amount paid to the club by a member who chose type B for the first n years Show that S 5,000,000 (1.1)-1+500,000n , where n is non-zero . 59 What is the minimum number of years a member should subscribe so that offer A become more advantageous than offer B